Question

The half-life of argon-39 is 269 years. It decays into krypton-39. After 1,076 years, what fraction of the original amount of argon-39 in a sample will still be argon

1/16
1/4
1/2
1/8

Answer 1

1/16

Step-by-step explanation:

From the question given above, the following data were obtained:

Half-life (t½) = 269 years

Time (t) = 1076 years

Fraction remaining =?

Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:

Half-life (t½) = 269 years

Time (t) = 1076 years

Number of half-lives (n) =?

n = t / t½

n = 1076 / 269

n = 4

Thus, 4 half-lives has elapsed.

Finally, we shall determine the fraction of the original amount remaining. This can be obtained as follow:

Let N₀ be the original amount.

Let N be the amount remaining.

Number of half-lives (n) = 4

Fraction remaining (N/N₀ ) =?

N = 1/2ⁿ × N₀

N = 1/2⁴ × N₀

N = 1/16 × N₀

Divide both side by N₀

N/N₀ = 1/16

Thus, the fraction of the original amount remaining is 1/16